Can't boot from any device: Missing \Boot\BCD

With my relatively new PC (a few months) I suddenly can't boot in Windows anymore after a Windows update. I get the follow error:

0xc0000225: The Boot Configuration Data for your PC is missing or contains errors. File: \Boot\BCD

Trying to start recovery gets me the same error.

I have a recovery USB with a bunch of tools. I've tried all of them. Most of PE tools display the same BCD error. Windows 10 setup (both from original DVD as from USB) displays the following error:

Windows cannot read the <ProductKey> setting from the unattend answer file.

I can boot in "boot recovery disk" which is a small Ubuntu based recovery environment. The tool says "boot repaired", but the problem remains. In that environment I can read and write on the disk, so the (nvme) disk is at least not fully broken.

I've tried resetting the BIOS to the defaults.

I'm out of ideas. If I google the error codes, I only find instructions like starting recovery from installation media, doing /bootrec /rebuildbcd, etc. but I can't do any of these, as the installation media isn't starting either.

All help is appreciated!

Extra info: When I disconnect the nmve drive, the Windows setup dvd starts normally. Of course, that doesn't help me, but it at least shows the dvd is OK...